This invention relates to an axial cylinder machine in which a shaft is journaled in one end of a housing and a plurality of cylinders are mounted on the other end of the housing and are equally spaced around the axis of the shaft. A spider is mounted in the housing to swivel about a main swivel connection centered along the axis of the shaft. Arms project generally radially from the spider and the outer end of each arm is connected by a swivel connection to a rod the other end of which is connected by a swivel to the piston in a cylinder. A head offset from the shaft axis is journaled in a crank connected to the shaft whereby successive reciprocation of the pistons swivels the spider in a generally circular manner to cause the head to revolve about the axis of the shaft and to turn the latter through the crank. Conversely, the shaft may be turned to swivel the spider and reciprocate the pistons.